Does it top out at 60 or are you scared to twist it any further?

Do you still have the stock belt drive or has the bike been converted to use a chain?

Have you used a speedometer app on your phone to verify that you are getting a correct reading out of the stock speedo?  

Are you wide open throttle in 6th when you are getting the 60mph reading?

Stock belt drive. No I'm not wide open, but it gets really loud. I'm probably just scared. Yesterday it read 57 and my dad said he was going 60 and I was keeping up, and it was really loud but still not wide open. I could have gone further but I guess I am afraid of "breaking" the engine. No I have not tried android speedo but I have thought about it this weekend. I'll try that. It does seem loud though. Maybe its just me . it also backfires when I roll off the throttle at those speeds ( if I roll off pretty quick, if I slow throlle slow its fine"

Are you still running the stock muffler?
Some modified mufflers, or straight pipes will be stupidly loud.

A tune-up?,...  really no such thing on a single cylinder with electronic ignition...
They'll change yer' spark plug and charge you $100...

Tune-up, carb work, vale jobs,... none of it will decrease the rpm's at high speeds...
That is a fixed ratio... engine pulses to wheel rotation...

Just twist the throttle... (if the rpm's scare you... run it at 60 in 3rd, for a few minutes... then, 4th will sound lazy and easy...)...

Believe me,... at anything under 50mph, you are lugging the engine in 4th...
Just get used to the engine running in it's stride...

That's right...  As long as you don't try to go 60 in 1st,... you won't hurt this bike with rpm's...
You'll get more damage by lugging it, or having your idle speed too low....(it needs some rpm to keep oil pressure up)... So, no lopey slow idle... you want a smooth steady purr...
...and, check your oil level every tankful if you do much running over 70mph...
It will use a little oil at those speeds...that's normal...

MMMmmmmmm ..... lemme see here ..... Gots an 1987 year model that is 28 years old at this point in time, with no mods and a NOISY stock muffler (rotted out internally most likely) ....

.... sucker jest won't rev up past 60 mph unless he really really works on it.

First question -- are you still running the 28 year old stock vac petcock ????    Has the air filter ever been cleaned/changed  ????

He's running in essence a straight pipe while sucking his gas through a 28 year old stock vac petcock and an unknown possibly clogged up air filter.

........ mmmmm ????   What comes to mind boys and girls?

I'd get him to blow out or replace his air filter and TEST/REPLACE his petcock (get a Raptor preferably) before I'd try to tell him anything else, because until those two thing are right you are off chasing them durn butterflies again.